CN107703285A - Asphalt complex modulus strain based on temperature parameter relies on model and determines method - Google Patents

Abstract

Model, which is relied on, the present invention relates to the strain of the asphalt complex modulus based on temperature parameter determines method, according to differently strained level, different loading frequencies, asphalt complex modulus result of the test at a temperature of different tests, by it is differently strained it is horizontal under a certain frequency when temperature and complex modulus Boltzmann functional relations on the basis of curve, the Temperature Shift factor being calculated by time temperature equivalence principle, translation processing is carried out to the temperature under other frequencies and complex modulus test data, it is temperature and strain level that independent variable is established based on this data, dependent variable relies on model for the asphalt complex modulus strain of complex modulus logarithm, as shown in formula (1).The model is using temperature and the complex modulus two-parameter, that asphalt is characterized by functional relation of strain, so that Modulus is changed into functional form, it effectively prevent pavement structure calculating analysis Asphalt Mixture modulus and be taken as definite value, the irrational problem of caused Calculation Anaysis for Tunnel Structure. $E=f(\mathrm{\ϵ},T)=a\·e^{c\·\mathrm{\ϵ}}+\frac{a\·e^{b\·\mathrm{\ϵ}}-a\·e^{c\·\mathrm{\ϵ}}}{1+e^{(T-x_0)/\mathrm{dx}}}---\left(1\right)$

Description

Asphalt complex modulus strain based on temperature parameter relies on model and determines method

Technical field

The invention mainly relates to field of road, more particularly to pavement structure calculates analysis Asphalt Mixture modulus Value is with determining problem.

Background technology

Modulus is one of key parameter in pavement structure calculating analysis, and its value directly affects force analysis knot Fruit.For perfect elastic body, modulus is the build-in attribute of material, is not changed with the change of stress or strain, generally Definite value, when carrying out pavement structure calculating analysis at present, each pavement layer modulus value is also definite value.It is however, substantial amounts of indoor and existing Field experiment shows that, due to constituent qualitative diversity and complexity, ground surface material typically exhibits anisotropism and anisotropy, The modulus of most ground surface materials can change with the change of stress or strain level, show fairly obvious stress or Dependency characteristic is strained, the modulus of ground surface material is not definite value, but a function expression relevant with stress or strain, i.e. mould The stress of amount or strain rely on model.In order to ensure the reasonability of pavement structure Calculation results, it is necessary to obtain road surface material The stress of material or strain rely on model, and carry out pavement structure accordingly and calculate analysis.

Complex modulus is the major parameter for characterizing structural response under asphalt alternate strain, can construct asphalt Complex modulus strain relies on the Modulus foundation that model calculates analysis as pavement structure.

The content of the invention

The present invention relies on model for the asphalt complex modulus strain based on temperature parameter and determines method, using temperature and Complex modulus two-parameter, that asphalt is characterized by function model is strained, the more existing definite value modulus of this method more meets road The actual conditions of face structure.

Asphalt complex modulus strain based on temperature parameter relies on model and determines method, comprises the following steps：

1) in differently strained horizontal ε_i(i=1 ..., n), different loading frequency f_j(j=1 ..., m), different tests temperature T_k Asphalt complex modulus experiment is carried out under (k=1 ..., p)；Wherein parameter i represents strain level level, parameter n represents strain Horizontal level sample total, parameter j represents loading frequency level, parameter m represents loading frequency level sample total, parameter k generations Watch test temperature level, parameter p represent test temperature level sample total, and n, m, p is positive integer.

2) obtain the frequency on the basis of a certain frequency by the following method, it is differently strained it is horizontal under, based on temperature parameter Asphalt complex modulus principal curve；

(1) in certain strain level ε_iUnder, temperature is answered with asphalt when characterizing a certain frequency using Boltzmann functions The dependency relation of log modulus,

(2) on the basis of the Boltzmann functional relations in (1), the Temperature Shift factor is introduced according to time temperature equivalence principle α_i,j(i=1 ..., n；J=1 ..., m), by strain level ε_iUnder, other frequencies when temperature and complex modulus test data carry out Translation is handled, and obtains temperature-complex modulus experiment after one group of new translation,

(3) regression analysis is carried out to the data in (2) using formula (1), can obtain using a certain frequency as reference frequency, should Become level as ε_iWhen, the asphalt complex modulus principal curve based on temperature parameter, function expression is formula (1),

In formula：T --- temperature, unit are DEG C；

E --- with 10 for bottom asphalt complex modulus logarithm；

A₁、A₂、x₀, dx --- regression parameter,

(4) using (1), (2), the method in (3), can obtain under other strain levels, on the basis of a certain frequency frequency, Asphalt complex modulus principal curve based on temperature parameter,

3) by temperature-complex modulus test data after the translation under differently strained level in step 2), being organized into independent variable is Temperature and strain level, the data format that dependent variable is complex modulus logarithm, carry out regression analysis to it using formula (2), can obtain Asphalt complex modulus strain based on temperature parameter relies on model；

In formula：T --- temperature, unit are DEG C；

E --- with 10 for bottom asphalt complex modulus logarithm；

ε --- strain, unit are 1 × 10²με；

a、b、c、x₀, dx --- regression parameter.

Strain level in the step 1) is 30,60,90,120,150 μ ε, loading frequency is usually 10,15,20,25, 30th, 35,40Hz, test temperature is usually 0,5,10,15,20,25,30,35,40,45 DEG C.

The reference frequency is 10Hz.

The model is using temperature and the complex modulus two-parameter, that asphalt is characterized by functional relation of strain so that Modulus is changed into functional form, effectively prevent pavement structure calculating analysis Asphalt Mixture modulus and is taken as definite value, is made Into the irrational problem of Calculation Anaysis for Tunnel Structure.

Brief description of the drawings

Temperature and the Boltzmann functional relations of complex modulus (the μ ε of strain level 30) during Fig. 1 frequency 10Hz,

Temperature and complex modulus test data translation result are (bent on the basis of μ ε of strain level 30,10Hz during Fig. 2 different frequencies Line),

Asphalt complex modulus principal curves (strain level 30 μ ε, 10Hz on the basis of curve) of the Fig. 3 based on temperature parameter,

Asphalt complex modulus principal curve under Fig. 4 whole strain levels based on temperature parameter is (on the basis of 10Hz frequently Rate).

Embodiment

By taking asphalt AH70-AC25 as an example, illustrate that the asphalt complex modulus strain based on temperature parameter relies on Model determines method, comprises the following steps that：

Step 1. carries out asphalt AH70-AC25 complex modulus experiment, the μ of strain level 30,60,90,120,150 ε, loading frequency 10,15,20,25,30,35,40Hz, test temperature 0,5,10,15,20,25,30,35,40,45 DEG C, institute Obtained asphalt complex modulus result of the test is shown in Table 1.Complex modulus data in table 1 are taken the logarithm, the results are shown in Table 2.

The asphalt AH70-AC25 complex modulus result of the tests of table 1

The asphalt AH70-AC25 complex modulus result of the test of table 2 (complex modulus is taken the logarithm)

Step 2. according to following step obtain strain level be 30 μ ε when, on the basis of 10Hz frequency, based on temperature parameter Asphalt complex modulus principal curve.

(1) based on data in table 2, using Boltzmann functions, when to establish strain level be 30 μ ε, frequency 10Hz Temperature and the relation of asphalt complex modulus logarithm, as shown in Figure 1.

(2) curve on the basis of temperature during frequency 10Hz and the Boltzmann functional relations of complex modulus, according to time temperature equivalence Principle calculates the Temperature Shift factor-alpha under each loading frequency_i,j(the results are shown in Table 2), by temperature during different frequency and complex modulus Test data is translated, and the result after translation is shown in Fig. 2 and table 3.

The Temperature Shift factor (the μ ε of strain level 30) under the different frequency of table 2

Temperature and complex modulus test data (the μ ε of strain level 30) after being translated under the different frequency of table 3

(3) regression analysis is carried out to the data of table 3 using formula (1), can obtain strain level when being 30 μ ε, based on temperature parameter Asphalt complex modulus principal curve (as shown in Figure 3), principal curve expression formula is shown in formula (3).

Step 3. according to the method for step 2 can to obtain strain level be 60,90,120,150 μ ε when, on the basis of 10Hz Frequency, the asphalt complex modulus principal curve based on temperature parameter, as shown in Figure 4.Each regression parameter number in principal curve Value is shown in Table 4.

The differently strained horizontal lower temperature of table 4 and the regression parameter in complex modulus principal curve relation

Regression parameter	30με	60με	90με	120με	150με
						A1	4.5681	4.5770	4.6071	4.6283	4.5974
A2	2.1896	1.9086	1.6340	1.4545	1.4919
						x0	31.4963	33.2646	34.8976	35.3059	34.4551
dx	14.2796	14.6466	15.7005	16.7262	16.6351

Step 4. descends differently strained level in step 3 the translation result of temperature and complex modulus test data, is organized into certainly The data format that variable is temperature and strain level, dependent variable are complex modulus logarithm, is shown in Table 5.

The differently strained horizontal lower temperature of table 5 and complex modulus test data translation result sorting table

Step 5. carries out regression analysis using formula (2) to data in table 5, can obtain asphalt AH70-AC25 and is based on The asphalt complex modulus strain of temperature parameter relies on model, sees formula (4).

Claims (3)

1. the asphalt complex modulus strain based on temperature parameter relies on model and determines method, comprise the following steps：

1) in differently strained horizontal ε_i(i=1 ..., n), different loading frequency f_j(j=1 ..., m), different tests temperature T_k(k= 1 ..., p) under carry out asphalt complex modulus experiment；Wherein parameter i represents strain level level, parameter n represents strain level Level sample total, parameter j represents loading frequency level, parameter m represents loading frequency level sample total, and parameter k represents examination Test temperature level, parameter p represents test temperature level sample total, n, m, p is positive integer.

2) obtain the frequency on the basis of a certain frequency by the following method, it is differently strained it is horizontal under, the pitch based on temperature parameter Compound complex modulus principal curve；

(1) in certain strain level ε_iUnder, temperature and asphalt complex modulus when characterizing a certain frequency using Boltzmann functions The dependency relation of logarithm,

(2) on the basis of the Boltzmann functional relations in step (1), the Temperature Shift factor is introduced according to time temperature equivalence principle α_i,j, wherein i=1 ..., n；J=1 ..., m, by strain level ε_iUnder, other frequencies when temperature and the test data of complex modulus enter Row translation is handled, and obtains temperature-complex modulus experiment after one group of new translation,

(3) regression analysis is carried out to the data in step (2) using formula (1), obtained using a certain frequency as reference frequency, strained Level is ε_iWhen, the asphalt complex modulus principal curve based on temperature parameter, function expression is formula (1),

In formula：T --- temperature, unit are DEG C；

E --- with 10 for bottom asphalt complex modulus logarithm；

A₁、A₂、x₀, dx --- regression parameter,

(4) using step (1), (2), the method in (3), can obtain under other strain levels, on the basis of a certain frequency frequency, Asphalt complex modulus principal curve based on temperature parameter,

3) by temperature-complex modulus test data after the translation under differently strained level in step 2), it is temperature to be organized into independent variable With strain level, the data format that dependent variable is complex modulus logarithm, regression analysis is carried out to it using formula (2), can be based on The asphalt complex modulus strain of temperature parameter relies on model；

In formula：T --- temperature, unit are DEG C；

E --- with 10 for bottom asphalt complex modulus logarithm；

ε --- strain, unit are 1 × 10²με；

a、b、c、x₀, dx --- regression parameter.

2. determination method according to claim 1, the strain level in the step 1) is 30,60,90,120,150 μ ε, Loading frequency is usually 10,15,20,25,30,35,40Hz, test temperature is usually 0,5,10,15,20,25,30,35,40, 45℃。

3. determination method according to claim 2, the reference frequency is 10Hz.